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In this remarkable paper, a team at DeepMind and Terence Tao addressed a fundamental challenge in mathematics using an AI system called AlphaEvolve. The challenge is the following: Many practical math problems ask "what's the best possible arrangement?"—like packing the most circles in a square or finding the largest set of points with no isosceles triangles—and answering these requires actually finding specific examples from search spaces so large that systematically exploring them by hand is impractical. AlphaEvolve doesn't have the LLM directly generate candidate solutions (which would require millions of expensive LLM calls to explore the search space)—instead, it evolves Python programs that search for solutions, so one expensive LLM call generates a search heuristic that then runs cheaply for millions of iterations exploring candidate configurations, and the population of these search programs evolves over time with better ones surviving, essentially doing meta-optimization where the thing being optimized is itself an optimizer. Across 67 problems spanning combinatorics, geometry, and analysis, AlphaEvolve discovered new constructions improving decades-old results (hexagon packing, Heilbronn triangles, sum-product problems) while matching state-of-the-art in dozens of others. The paper reports every problem they tried including failures where AlphaEvolve couldn't match known bounds, which makes this the most thorough empirical evaluation of AI for mathematical discovery. Read and ask questions on ChapterPal: chapterpal.com/s/c9843ce4/ma… Download the PDF: arxiv.org/pdf/2511.02864